I will discuss our recently-proposed model (hep-th/1106.3566) of deformations of general relativity that are consistent and potentially phenomenologically viable, since they respect cosmological backgrounds. These deformations have unique symmetries in accordance with unitarity requirements, and give rise to a curvature induced self-stabilizing mechanism. Furthermore, our findings include the possibility of consistent and potentially phenomenologically viable deformations of general relativity that are solely operative on curved spacetime geometries, reducing to Einstein’s theory on the Minkowski background. I will also comment on possible phenomenological implications.